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Correlation Integral

Consider a set of points X_i on an attractor, then the correlation integral is

C(l)=lim_(N->infty)1/(N^2)f,

where f is the number of pairs (i,j) whose distance |X_i-X_j|<l. For small l,

C(l)∼l^nu,

where nu is the correlation exponent.

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References

Grassberger, P. and Procaccia, I. "Measuring the Strangeness of Strange Attractors." Physica D 9, 189-208, 1983.

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Correlation Integral

Cite this as:

Weisstein, Eric W. "Correlation Integral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CorrelationIntegral.html

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